Question

1.
if F(x,y) = ye^x + e^x. find the integral over C of F * dr when C
consists of the line segments 0,1) to (0,2) and (0,2) to
(4,2)

Answer #1

Evaluate the vector line integral F*dr of F(x,y) = <xy,y>
along the line segment K from the point (2,0) to the point (0,2) in
the xy-plane

given field F =[x+y, 2xy ] and c: x= y^2
calculate the line integral along (1,-1) to (4,2)

(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y>
conservative?
(b) If so, find the associated potential function φ.
(c) Evaluate Integral C F*dr, where C is the straight line path
from (0, 0) to (2π, 2π).
(d) Write the expression for the line integral as a single
integral without using the fundamental theorem of calculus.

Let F = (sin(x 3 ), 2yex 2 ). Evaluate the line integral Z C F ·
dr, where C consists of two line segments, which go from (0, 0) to
(2, 2), and then from (2, 2) to (0, 2).

1.) Let f(x,y) =x^2+y^3+sin(x^2+y^3). Determine the line
integral of f(x,y) with respect to arc length over the unit circle
centered at the origin (0, 0).
2.)
Let f ( x,y)=x^3+y+cos( x )+e^(x − y). Determine the line
integral of f(x,y) with respect to arc length over the line segment
from (-1, 0) to (1, -2)

Find the absolute maximum, and minimum values of the function:
f(x, y) = x + y − xy Defined over the closed rectangular region D
with vertices (0,0), (4,0), (4,2), and (0,2)

(1 point)
Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=3xi+4yj-zk
and C is given by the vector function r(t)=〈sint,cost,t〉,
0≤t≤3π/2.

(9)
(a)Find the double integral of the function f (x, y) = x + 2y
over the region in the plane bounded by the lines x = 0, y = x, and
y = 3 − 2x.
(b)Find the maximum and minimum values of 2x − 6y + 5 subject to
the constraint x^2 + 3(y^2) = 1.
(c)Consider the function f(x,y) = x^2 + xy. Find the directional
derivative of f at the point (−1, 3) in the direction...

Evaluate the line integral F * dr where F = 〈2xy, x^2〉 and the
curve C is the trajectory of rt = 〈4t−3, t^2〉 for −1 ≤ t≤1.

Let fx,y (x,y) = 3 e^-(x+y) for 0 < x <1/2y and y>0. a)
Find f x(x) and f y( y) . b) Write out the integral
necessary to find , Fx,y ( u v) . DO NOT EVALUATE THE INTEGRAL.

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